Data Structures:

1. (a) Construct an AVL tree for the list 7, 15, 3, 19, 21, 13, 2. Use the alphabetical ascending order of the letters and insert them successively starting with the empty tree. Your answer should present the rotation operations clearly for each letter addition.

[Note: If it is difficult to draw the trees on the word file, draw them on paper by hand. Then take a picture of the paper and attach the picture here.]

(b) Assuming that the probabilities of searching for each of the keys (i.e., the letters) are the same, find the largest number and the average number of key comparisons for successful searches on the AVL tree you constructed in the question (a).